def test_search_descending():
a = np.linspace(10., 1., 10)
npt.assert_equal(search_descending(a, 1.), 1)
npt.assert_equal(search_descending(a, .89), 2)
npt.assert_equal(search_descending(a, .79), 3)
# Test small array
npt.assert_equal(search_descending(a[:1], 1.), 1)
npt.assert_equal(search_descending(a[:1], 0.), 1)
npt.assert_equal(search_descending(a[:1], .5), 1)
# Test very small array
npt.assert_equal(search_descending(a[:0], 1.), 1)
def test_search_descending():
a = np.linspace(10., 1., 10)
npt.assert_equal(search_descending(a, 1.), 1)
npt.assert_equal(search_descending(a, .89), 2)
npt.assert_equal(search_descending(a, .79), 3)
# Test small array
npt.assert_equal(search_descending(a[:1], 1.), 1)
npt.assert_equal(search_descending(a[:1], 0.), 1)
npt.assert_equal(search_descending(a[:1], .5), 1)
# Test very small array
npt.assert_equal(search_descending(a[:0], 1.), 0)
def peak_directions(odf,
sphere,
relative_peak_threshold=.5,
min_separation_angle=25,
minmax_norm=True):
"""Get the directions of odf peaks
Peaks are defined as points on the odf that are greater than at least one
neighbor and greater than or equal to all neighbors. Peaks are sorted in
descending order by their values then filtered based on their relative size
and spacing on the sphere. An odf may have 0 peaks, for example if the odf
is perfectly isotropic.
Parameters
----------
odf : 1d ndarray
The odf function evaluated on the vertices of `sphere`
sphere : Sphere
The Sphere providing discrete directions for evaluation.
relative_peak_threshold : float in [0., 1.]
Only peaks greater than ``min + relative_peak_threshold * scale`` are
kept, where ``min = max(0, odf.min())`` and
``scale = odf.max() - min``.
min_separation_angle : float in [0, 90]
The minimum distance between directions. If two peaks are too close
only the larger of the two is returned.
Returns
-------
directions : (N, 3) ndarray
N vertices for sphere, one for each peak
values : (N,) ndarray
peak values
indices : (N,) ndarray
peak indices of the directions on the sphere
Notes
-----
If the odf has any negative values, they will be clipped to zeros.
"""
values, indices = local_maxima(odf, sphere.edges)
# If there is only one peak return
n = len(values)
if n == 0 or (values[0] < 0.):
return np.zeros((0, 3)), np.zeros(0), np.zeros(0, dtype=int)
elif n == 1:
return sphere.vertices[indices], values, indices
odf_min = odf.min()
odf_min = odf_min if (odf_min >= 0.) else 0.
# because of the relative threshold this algorithm will give the same peaks
# as if we divide (values - odf_min) with (odf_max - odf_min) or not so
# here we skip the division to increase speed
values_norm = (values - odf_min)
# Remove small peaks
n = search_descending(values_norm, relative_peak_threshold)
indices = indices[:n]
directions = sphere.vertices[indices]
# Remove peaks too close together
directions, uniq = remove_similar_vertices(directions,
min_separation_angle,
return_index=True)
values = values[uniq]
indices = indices[uniq]
return directions, values, indices
def peak_directions_nl(sphere_eval,
relative_peak_threshold=.25,
min_separation_angle=25,
sphere=default_sphere,
xtol=1e-7):
"""Non Linear Direction Finder
Parameters
----------
sphere_eval : callable
A function which can be evaluated on a sphere.
relative_peak_threshold : float
Only return peaks greater than ``relative_peak_threshold * m`` where m
is the largest peak.
min_separation_angle : float in [0, 90]
The minimum distance between directions. If two peaks are too close
only the larger of the two is returned.
sphere : Sphere
A discrete Sphere. The points on the sphere will be used for initial
estimate of maximums.
xtol : float
Relative tolerance for optimization.
Returns
-------
directions : array (N, 3)
Points on the sphere corresponding to N local maxima on the sphere.
values : array (N,)
Value of sphere_eval at each point on directions.
"""
# Find discrete peaks for use as seeds in non-linear search
discrete_values = sphere_eval(sphere)
values, indices = local_maxima(discrete_values, sphere.edges)
seeds = np.column_stack([sphere.theta[indices], sphere.phi[indices]])
# Helper function
def _helper(x):
sphere = Sphere(theta=x[0], phi=x[1])
return -sphere_eval(sphere)
# Non-linear search
num_seeds = len(seeds)
theta = np.empty(num_seeds)
phi = np.empty(num_seeds)
for i in xrange(num_seeds):
peak = opt.fmin(_helper, seeds[i], xtol=xtol, disp=False)
theta[i], phi[i] = peak
# Evaluate on new-found peaks
small_sphere = Sphere(theta=theta, phi=phi)
values = sphere_eval(small_sphere)
# Sort in descending order
order = values.argsort()[::-1]
values = values[order]
directions = small_sphere.vertices[order]
# Remove directions that are too small
n = search_descending(values, relative_peak_threshold)
directions = directions[:n]
# Remove peaks too close to each-other
directions, idx = remove_similar_vertices(directions,
min_separation_angle,
return_index=True)
values = values[idx]
return directions, values
def peak_directions(odf, sphere, relative_peak_threshold=.5,
min_separation_angle=25, minmax_norm=True):
"""Get the directions of odf peaks.
Peaks are defined as points on the odf that are greater than at least one
neighbor and greater than or equal to all neighbors. Peaks are sorted in
descending order by their values then filtered based on their relative size
and spacing on the sphere. An odf may have 0 peaks, for example if the odf
is perfectly isotropic.
Parameters
----------
odf : 1d ndarray
The odf function evaluated on the vertices of `sphere`
sphere : Sphere
The Sphere providing discrete directions for evaluation.
relative_peak_threshold : float in [0., 1.]
Only peaks greater than ``min + relative_peak_threshold * scale`` are
kept, where ``min = max(0, odf.min())`` and
``scale = odf.max() - min``.
min_separation_angle : float in [0, 90]
The minimum distance between directions. If two peaks are too close
only the larger of the two is returned.
Returns
-------
directions : (N, 3) ndarray
N vertices for sphere, one for each peak
values : (N,) ndarray
peak values
indices : (N,) ndarray
peak indices of the directions on the sphere
Notes
-----
If the odf has any negative values, they will be clipped to zeros.
"""
values, indices = local_maxima(odf, sphere.edges)
# If there is only one peak return
n = len(values)
if n == 0 or (values[0] < 0.):
return np.zeros((0, 3)), np.zeros(0), np.zeros(0, dtype=int)
elif n == 1:
return sphere.vertices[indices], values, indices
odf_min = np.min(odf)
odf_min = odf_min if (odf_min >= 0.) else 0.
# because of the relative threshold this algorithm will give the same peaks
# as if we divide (values - odf_min) with (odf_max - odf_min) or not so
# here we skip the division to increase speed
values_norm = (values - odf_min)
# Remove small peaks
n = search_descending(values_norm, relative_peak_threshold)
indices = indices[:n]
directions = sphere.vertices[indices]
# Remove peaks too close together
directions, uniq = remove_similar_vertices(directions,
min_separation_angle,
return_index=True)
values = values[uniq]
indices = indices[uniq]
return directions, values, indices
def peak_directions_nl(sphere_eval, relative_peak_threshold=.25,
min_separation_angle=25, sphere=default_sphere,
xtol=1e-7):
"""Non Linear Direction Finder.
Parameters
----------
sphere_eval : callable
A function which can be evaluated on a sphere.
relative_peak_threshold : float
Only return peaks greater than ``relative_peak_threshold * m`` where m
is the largest peak.
min_separation_angle : float in [0, 90]
The minimum distance between directions. If two peaks are too close
only the larger of the two is returned.
sphere : Sphere
A discrete Sphere. The points on the sphere will be used for initial
estimate of maximums.
xtol : float
Relative tolerance for optimization.
Returns
-------
directions : array (N, 3)
Points on the sphere corresponding to N local maxima on the sphere.
values : array (N,)
Value of sphere_eval at each point on directions.
"""
# Find discrete peaks for use as seeds in non-linear search
discrete_values = sphere_eval(sphere)
values, indices = local_maxima(discrete_values, sphere.edges)
seeds = np.column_stack([sphere.theta[indices], sphere.phi[indices]])
# Helper function
def _helper(x):
sphere = Sphere(theta=x[0], phi=x[1])
return -sphere_eval(sphere)
# Non-linear search
num_seeds = len(seeds)
theta = np.empty(num_seeds)
phi = np.empty(num_seeds)
for i in xrange(num_seeds):
peak = opt.fmin(_helper, seeds[i], xtol=xtol, disp=False)
theta[i], phi[i] = peak
# Evaluate on new-found peaks
small_sphere = Sphere(theta=theta, phi=phi)
values = sphere_eval(small_sphere)
# Sort in descending order
order = values.argsort()[::-1]
values = values[order]
directions = small_sphere.vertices[order]
# Remove directions that are too small
n = search_descending(values, relative_peak_threshold)
directions = directions[:n]
# Remove peaks too close to each-other
directions, idx = remove_similar_vertices(directions, min_separation_angle,
return_index=True)
values = values[idx]
return directions, values
